Failure of continuous fiber composites are much more complex than metal. Continuous fiber structure involves most of the time stacking of several plies, each ply being characterized by a single fiber orientation. The intra-laminar failure mechanism is mainly due to delamination, while the inter-laminar failure is governed by various mechanisms like matrix cracking, fiber breakage or fiber-matrix debonding Figure 1 illustrates the source of inter-laminar failure as function of the fiber orientation.
The capture of these complex phenomena requires an approach allowing the prediction of the failure of the composite but also its progressive damage. Neglect the progressive damage of the composite is equivalent to model the composite as a brittle material what does not correspond to the reality. Failure can start at the level of the resin leading to a drop of stiffness but the composite still show strength due to the fibers.
A promising approach to model the progressive damage of the composite is to use a micro-macro approach. Such an approach is using the material behavior of each constituent to predict the behavior of the resultant composite by taking into account the microstructure (fiber amount and fiber orientation). This solution leads to a more accurate stress and strain pattern in the composite and therefore to a better prediction of the damage and failure of the composite.
The failure of the composite at the level of the ply can be predicted by using the Hashin failure criterion associated to a progressive damage model like the model proposed by Matzenmiller-Lubliner-Taylor. The Hashin failure criteria is based on four failure criteria: fa, fb, fc and fd. fa and fb are governed by the failure of the fibers in tension and compression respectively. The failure of the resin in tension and in compression controls the evolution of fc and fd respectively. As soon as one of these failure criteria reaches a value larger than one, the corresponding damage parameter starts to increase. Damage in the fiber is a function of fa and fb, damage in the matrix a function of fc and fd and finally the damage in shear is a function of the damage in the fiber and the damage in the matrix. The damage functions can be linear, exponential or instantaneous as illustrated in the figure 2.This brief description shows the richness of this damage model.
The calibration of this model requires few experimental data measured on plain coupon. Coupon is here a lamina and not a laminate. Each test must be performed till the failure of the lamina and the evolution of the force vs. displacement must be tracked. This force/displacement is then transformed in a stress-strain curve to calibrate the material model in term of stiffness. The failure and damage model is calibrated in a second step from the failure observed during the test. A minimum of five coupon are needed:
- Two coupon at 0° to evaluate the stiffness and strength in tension and compression of the lamina. These results will be governed mainly by the fiber strength.
- Two coupon at 90° to evaluate the stiffness and strength in tension and compression of a transverse lamina. These results will be governed mainly by the resin strength.
- One coupon at 45° to evaluate the stiffness and strength in shear of the lamina.
This model is, of course, not limited to the failure prediction of coupon but can be used on any type of composite component. The progressive damage model available in Digimat, the multi-scale material modeling platform developed by e-Xstream engineering is based on this approach and can be coupled with many FEA programs such as MSC Nastran and Marc to predict the failure of complex component.
If you would like to learn more, feel free to write me at . Please include a link to this blog post when writing.